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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 2, Pages 403–411 (Mi tvp294)  

This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

Integral Equations and Phase Transitions in Stochastic Games. An Analogy with Statistical Physics

V. P. Maslov

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: Maximization of the Kullback–Leibler information is known to result in general Esscher transformations. The Bose–Einstein and Fermi–Dirac statistics in a probability space $(\Omega, \mathcal{F},P)$ give rise to another kind of information, namely,
$$ S_B=\int \log(1+\frac{dP}{dQ}) dQ+ \int \log(1+\frac{dQ}{dP}) dP $$
for the Bose statistics and
$$ S_F =\int\log(\frac{dP}{dQ}-1) dQ -\int\log(1-\frac{dQ}{dP}) dP, \qquad \frac{dP}{dQ} >1, $$
for the Fermi statistics. This information generates measure transformations corresponding to these statistics. In the presence of a payoff matrix, these transformations vary in accordance with the integral equations given in the paper. We give examples of financial games corresponding to Bose and Fermi statistics.

Keywords: Bose statistics, Fermi statistics, payoff matrix, Esscher transformation, entropy, phase transition, integral equation, Kullback–Leibler information, thermodynamics, statistical physics, dyadic games.

DOI: https://doi.org/10.4213/tvp294

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English version:
Theory of Probability and its Applications, 2004, 48:2, 359–367

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Received: 17.03.2003

Citation: V. P. Maslov, “Integral Equations and Phase Transitions in Stochastic Games. An Analogy with Statistical Physics”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 403–411; Theory Probab. Appl., 48:2 (2004), 359–367

Citation in format AMSBIB
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\by V.~P.~Maslov
\paper Integral Equations and Phase Transitions in Stochastic Games. An Analogy with Statistical Physics
\jour Teor. Veroyatnost. i Primenen.
\yr 2003
\vol 48
\issue 2
\pages 403--411
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2015462}
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 2
\pages 359--367
\crossref{https://doi.org/10.1137/S0040585X97980464}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Maslov, “Nonlinear financial averaging, the evolution process, and laws of econophysics”, Theory Probab. Appl., 49:2 (2005), 221–244  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. P. Maslov, “Nonlinear Averages in Economics”, Math. Notes, 78:3 (2005), 347–363  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. V. V'yugin, V. P. Maslov, “Theorems on Concentration for the Entropy of Free Energy”, Problems Inform. Transmission, 41:2 (2005), 134–149  mathnet  crossref  mathscinet  zmath  elib  elib
    4. V. V. V'yugin, V. P. Maslov, “Distribution of Investments in the Stock Market, Information Types, and Algorithmic Complexity”, Problems Inform. Transmission, 42:3 (2006), 251–261  mathnet  crossref  mathscinet  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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